Q: What are the factor combinations of the number 1,212,215?

 A:
Positive:   1 x 12122155 x 24244323 x 5270583 x 14605115 x 10541127 x 9545415 x 2921635 x 1909
Negative: -1 x -1212215-5 x -242443-23 x -52705-83 x -14605-115 x -10541-127 x -9545-415 x -2921-635 x -1909


How do I find the factor combinations of the number 1,212,215?

Unfortunately, there's not simple formula to identifying all of the factors of a number and it can be a tedious process when trying to identify the divisors of larger numbers. To find the factor combinations of the number 1,212,215, it is easier to work with a table - it's called factoring from the outside in.

Outside in Factoring

We start by creating a table and writing 1 on the left side and then the number we're trying to find the factors for on the right side in a table. Then, below that, write the numbers as a negative as well.

1 1,212,215
-1 -1,212,215

Why are the negative numbers included?

When you multiply two negative numbers together, you get a positive number. That means both the positive and negative numbers are factors of 1,212,215.

Example:
1 x 1,212,215 = 1,212,215
and
-1 x -1,212,215 = 1,212,215
Notice both answers equal 1,212,215

With that explanation out of the way, let's continue. Next, we take the number 1,212,215 and divide it by 2:

1,212,215 ÷ 2 = 606,107.5

If the quotient is a whole number, then 2 and 606,107.5 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,212,215
-1 -1,212,215

Now, we try dividing 1,212,215 by 3:

1,212,215 ÷ 3 = 404,071.6667

If the quotient is a whole number, then 3 and 404,071.6667 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,212,215
-1 -1,212,215

Let's try dividing by 4:

1,212,215 ÷ 4 = 303,053.75

If the quotient is a whole number, then 4 and 303,053.75 are factors. In this case, the quotient is not a whole number. Don't write anything down and try the next divisor.

Here is what our table should look like at this step:

1 1,212,215
-1 1,212,215
Keep dividing by the next highest number until you cannot divide anymore.

If you did it right, you will end up with this table:

1523831151274156351,9092,9219,54510,54114,60552,705242,4431,212,215
-1-5-23-83-115-127-415-635-1,909-2,921-9,545-10,541-14,605-52,705-242,443-1,212,215

More Examples

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